Tagged Questions

Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...

From the answer to this question Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, I have discovered that there is two perspectives to QFT. I am doing a course which is unfortunately a summary of QFT and ...

Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path ...

I've recently been reading Path Integrals and Quantum Processes by Mark Swanson; it's an excellent and pedagogical introduction to the Path Integral formulation.
He derives the path integral and shows ...

Consider a system of two spins $s_1$ and $s_2$, each of which can be in one of two states, represented by 0 or 1. A basis for the Hilbert space of this system would be {|0,0>,|0,1>,|1,0> and |1,1>}, ...

I want to learn how to do path integrals as used in quantum field theory. I understand the specific type of integral used in qft is called a functional integral. I looked at Wikipedia and checked in ...

Mathematically, what is the kernel in path integral? At first, I thought that it is the kernel in the integral transform because when we use the (physical) kernel to transform the wave function (Eq ...

In a physics paper (here) I found this variant of the Bessel function of the first kind.
$$ \tag{1} Z(g) ~=~ \frac{1}{\sqrt{g}} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{-\frac{1}{2g} \sin^2 x} \, dx
...

In his Quantum Field Theory In a Nutshell, in page 12, (Second Ed), A Zee says that conventionally, the amplitude $\langle0|e^{-iHT}|0\rangle$ is denoted by $Z$. In the next paragraph, he considers ...

I have been working on a quantum mechanics problem I asked here and someone recommended to use path integrals. I learned about path integrals but I couldn't find out how to finding the most optimized ...

In Kerson Huang's Quantum Field Theory From Operators to Path Integrals (Amazon link), pages 28 and 29, he calculates the propagator in the following case: time-like, space-like and light-like. First ...

I was recently considering a problem analogous to the Aharonov-Bohm (AB) effect but in the context of quantum field theory. Consider then Dirac electrons minimally coupled to an AB flux and described ...

I was reading about path integrals because someone told me about it in this question. I read some articles about path integrals but couldn't understand it. Can you please explain path integral for me? ...

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...

I've been reading up on non-perturbative Yang-Mills, and have found the following equation:
$$Z[\gamma, g^2, G]=\int \! \prod e^{-S}\mathrm{d}U_i$$
Now I don't know much about computational physics, ...

The generating functional for a free Dirac field is
$$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$
where ...

Recently I've read that background field gauge is very convenient for gauge theories, because it fixes the connection between normalization constants of gauge field and gauge coupling constant one. I ...

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...